Of you read more recent books about computers, they just talk about the Internet. The reason that a bunch of different networks (AOL, Compuserve, Prodigy, WorldNet, UUNet, etc.) all could be talked about as the Internet, not just a bunch of internets, is not just a product of random chance, or anything inherent to computer networks.
It relates specifically to the ways that a group of very smart people worked to create the rules of networking. Coming from an academic background, their desire was to create networks that were easy to join and architectures that made it hard not to share. The major network providers were discouraged, in both formal ways and through informal norms, from giving preference to one network provider over another. I access the Internet at home through Sunflower Broadband, a Lawrence based provider.
When I access Google, I go from Sunflower's servers to the Sprint network, and on to Google. To get to Apple's website, I go through Level3's servers. Other websites send me through other network paths, and it doesn't matter because of something called "network neutrality." Network neutrality means that traffic from one provider (like little old Sunflower Broadband) isn't treated differently than traffic from another (like AOL). Without that, major services like Google would wither on the vine, and local ISPs would be in dire straits.
Without network neutrality, Google would have to cut a deal with every network provider to ensure that anyone who wanted to access their service would get fast service. And Sunflower Broadband would have to make deals with all the providers to make sure that data originating with them would actually reach its destination across however many network providers were necessary.
The Congress is currently considering a truly silly idea of ending network neutrality, allowing individual network providers to penalize traffic from different origins. Save the Internet explains more. This is worth calling a Congresscritter about.